Intrinsic spin Hall conductivity in one-, two-, and three-dimensional trivial and topological systems

Matthes, Lars; Küfner, Sebastian; Furthmüller, J.; Bechstedt, F.

doi:10.1103/physrevb.94.085410

Cited by 31 publications

(25 citation statements)

References 38 publications

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“…The computation for systems without inversion symmetry is performed using the method of Yu et al 32 as implemented in the VASP code 8 . The third-rank tensor of the intrinsic spin Hall conductivity σ i jk (ω) is calculated within the Kubo formalism 33 . We focus on the static limit ω → 0,…”

Section: Theoretical and Computational Methodsmentioning

confidence: 99%

Quantization of spin Hall conductivity in two-dimensional topological insulators versus symmetry and spin-orbit interaction

et al. 2019

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The third-rank tensor of the static spin Hall conductivity is investigated for two-dimensional (2D) topological insulators by electronic structure calculations. Its seeming quantization is numerically demonstrated for highly symmetric systems independent of the gap size. 2D crystals with hexagonal and square Bravais lattice show similar effects, while true rectangular translational symmetry yields conductivity values much below the quantum e 2 /h. Field-induced lifting the inversion symmetry does not influence the quantum spin Hall state up to band inversion but the conductivity quantization. Weak symmetry-conserving biaxial but also uniaxial strain has a minor influence as long as inverted gaps dictate the topological character. The results are discussed in terms of the atomic geometry and the Rashba contribution to the spin-orbit interaction (SOI). Translational and point-group symmetry as well as SOI rule the deviation from the quantization of the spin Hall conductance. :1909.11138v2 [cond-mat.mes-hall] arXiv

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Section: Theoretical and Computational Methodsmentioning

confidence: 99%

Quantization of spin Hall conductivity in two-dimensional topological insulators versus symmetry and spin-orbit interaction

et al. 2019

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“…The intrinsic SHE, significantly contributing to the total SHE in materials with strongly spin-orbit-coupled bands [1], can be calculated accurately based on ab-initio theories. According to the Kubo formula, the spin Hall conductivity (SHC) can be written as [10][11][12] σ spinz…”

Section: Introductionmentioning

confidence: 99%

Calculation of intrinsic spin Hall conductivity by Wannier interpolation

et al. 2018

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Ab-initio calculation of intrinsic spin Hall conductivity (SHC) generally requires a strict convergence criterion and a dense k-point mesh to sample the Brillouin zone, making its convergence challenging and time-consuming. Here we present a scheme for efficiently and accurately calculating SHC based on maximally localized Wannier function (MLWF). The quantities needed by the Kubo formula of SHC are derived in the space of MLWF and it is shown that only the Hamiltonian, the overlap and the spin operator matrices are required from the initial ab-initio calculation. The computation of these matrices and the interpolation of Kubo formula on a dense k-point mesh can be easily achieved. We validate our results by prototypical calculations on fcc Pt and GaAs, which demonstrate that the Wannier interpolation approach is of high accuracy and efficiency. Calculations of α-Ta and β-Ta show that SHC of β-Ta is 2.7 times of α-Ta, while both have the opposite sign relative to fcc Pt and are an order of magnitude smaller than Pt. The calculated spin Hall angle of −0.156, is quite consistent with previous experiment on β-Ta, further suggesting intrinsic contribution may dominate in β-Ta. Our approach could facilitate large-scale SHC calculations, and may benefit the discovery of materials with high intrinsic SHC. arXiv:1810.07637v1 [cond-mat.mtrl-sci] 17 Oct 2018 (0) nk to

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“…Because of the absence of inversion symmetry, we apply the method of Yu et al . 47 based on the evolution of the charge centers of the Wannier functions (WCC) between two time-reversal invariant momenta (TRIM) of the BZ 46 , 48 and implemented in the VASP code 18 , 49 . The topological invariant Z 2 is determined by the crossings of an arbitrary reference line modulo 2 connecting two TRIM points within the WCC phase evolution along the k y line 47 .…”

Section: Resultsmentioning

confidence: 99%

“…Although some lines in the WCC evolution appear to interconnect, the topological behavior is not clear. For germanene/graphene the presence of pair switchings simply give a topological invariant , which suggests that this system is a QSH phase 18 , 46 , 49 .…”

Section: Resultsmentioning

confidence: 99%

Deposition of topological silicene, germanene and stanene on graphene-covered SiC substrates

Matusalem

Koda

Bechstedt

et al. 2017

Sci Rep

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Growth of X-enes, such as silicene, germanene and stanene, requires passivated substrates to ensure the survival of their exotic properties. Using first-principles methods, we study as-grown graphene on polar SiC surfaces as suitable substrates. Trilayer combinations with coincidence lattices with large hexagonal unit cells allow for strain-free group-IV monolayers. In contrast to the Si-terminated SiC surface, van der Waals-bonded honeycomb X-ene/graphene bilayers on top of the C-terminated SiC substrate are stable. Folded band structures show Dirac cones of the overlayers with small gaps of about 0.1 eV in between. The topological invariants of the peeled-off X-ene/graphene bilayers indicate the presence of topological character and the existence of a quantum spin Hall phase.

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Intrinsic spin Hall conductivity in one-, two-, and three-dimensional trivial and topological systems

Cited by 31 publications

References 38 publications

Quantization of spin Hall conductivity in two-dimensional topological insulators versus symmetry and spin-orbit interaction

Quantization of spin Hall conductivity in two-dimensional topological insulators versus symmetry and spin-orbit interaction

Calculation of intrinsic spin Hall conductivity by Wannier interpolation

Deposition of topological silicene, germanene and stanene on graphene-covered SiC substrates

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